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arXiv · 1805.07552

Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors

René Ciak·Melanie Melching·Otmar Scherzer
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Abstract

We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such functions. These regularization functionals are motivated from double integrals, which approximate Sobolev semi-norms of intensity functions. These were introduced in Bourgain, Br\'ezis and Mironescu, "Another Look at Sobolev Spaces". In: Optimal Control and Partial Differential Equations-Innovations and Applications, IOS press, Amsterdam, 2001. For the proposed regularization functionals we prove existence of minimizers as well as a stability and convergence result for functions with values in a set of vectors.

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René Ciak, Melanie Melching, Otmar Scherzer. 2018-05-19. Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors. https://arxiv.org/abs/1805.07552

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